The third proportional to 0.36 and 0.48 is

Options

A. 0.64
B. 0.1728
C. 0.42
D. 0.99

Answer

To find the third proportional to the numbers 0.36 and 0.48, we can follow these steps:

### Step 1: Understand the concept of third proportional
The third proportional to two numbers A and B is a number X such that the ratio A:B is the same as the ratio B:X. This can be expressed mathematically as:
\[ \frac{A}{B} = \frac{B}{X} \]

### Step 2: Set up the equation
From the above ratio, we can rearrange the equation to find X:
\[ X = \frac{B^2}{A} \]

### Step 3: Substitute the values
In our case, A = 0.36 and B = 0.48. We can substitute these values into the equation:
\[ X = \frac{(0.48)^2}{0.36} \]

### Step 4: Calculate \(B^2\)
Now we need to calculate \(B^2\):
\[ (0.48)^2 = 0.48 \times 0.48 = 0.2304 \]

### Step 5: Divide by A
Now, we will divide \(0.2304\) by \(0.36\):
\[ X = \frac{0.2304}{0.36} \]

### Step 6: Perform the division
To perform the division, we can convert both numbers to eliminate the decimal:
\[ X = \frac{0.2304 \times 100}{0.36 \times 100} = \frac{23.04}{36} \]

Now, divide \(23.04\) by \(36\):
\[ X = 0.64 \]

### Conclusion
Thus, the third proportional to 0.36 and 0.48 is:
\[ \boxed{0.64} \]

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